Question

If there are 100 students in your class and everybody flips a coin five times, how many people are likely to get five heads in a row?
This is with the assumption that every time you flip a coin, the chance that heads will end up on top is 1 in 2.

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Answer 1

If you flip a coin once, you have a 1/2 chance of getting heads. You will get either a head or tail.

Flipping a coin twice gives you a 1/4 chance of getting 2 heads since you will either get a 2 heads, 2 tails, a tail then head, or a head then tails.

From this we can see its pretty likely the pattern will continue if our chances of continually getting a head keeps halfing. So we can represent it as 1/2^n (half to the power of n) where n is the number of times we flip the coin.

So the odds of flipping a coin 5 times and getting 5 heads are 1/2 ^5 (half to the power of 5). Which gives us 1/32 or just over a 3% chance.

Answer 2

Here we have a probability problem.

We will find that the expected number of students that gets 5 heads in a row is 3.

First, we need to find the probability of getting 5 heads in a row.

We assume that the probability of getting heads in a flip is p = 1/2 = 0.5

Then for getting heads 5 times in a row, the joint probability will be the product of the individual probabilities, we get:

$P = (0.5)*(0.5)*(0.5)*(0.5)*(0.5) = (0.5)^5 = 0.03125$

Now if we have N persons, such that all of them flip a coin 5 times, the expected number of people that will get 5 heads in a row will be equal to the total number of people times the probability of getting 5 heads in a row.

N*P

So if in the class there are 100 students, we have N = 100

The expected number of students that will get 5 heads in a row is:

$100*P = 100*0.03125 = 3.125$

Because we can have a 0.125 of a student, we need to round this to the nearest whole number, which is 3.

So we should expect that 3 students will get 5 heads in a row.

If you want to learn more, you can read:

https://brainly.com/question/17089724